Related papers: Free Versus Constrained Evolution of the 2+1 Equiv…
Perturbed Runge--Kutta methods (also referred to as downwind Runge--Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge--Kutta counterparts. In this paper we study, the question…
We establish global convergence of the (1+1) evolution strategy, i.e., convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the…
Compact Runge-Kutta (cRK) methods are a class of high order methods for solving hyperbolic conservation laws characterized by their compact stencil including only immediate neighboring finite elements. A Compact Runge-Kutta flux…
The efficiency of sampling-based motion planning brings wide application in autonomous mobile robots. The conventional rapidly exploring random tree (RRT) algorithm and its variants have gained significant successes, but there are still…
Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising…
We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations…
Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex.…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their…
We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be explicit and retain the accuracy and stability properties of the…
By combining Genetic Programming, MAP-Elites and Covariance Matrix Adaptation Evolution Strategy, we demonstrate very high success rates in Symbolic Regression problems. MAP-Elites is used to improve exploration while preserving diversity…
In this paper, exponential Runge-Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323-339, 2005) are extended to semilinear parabolic problems with time-dependent delay. Two classes of the ERKC…
The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…
An explicit numerical strategy that practically preserves invariants is derived for conservative systems by combining an explicit high-order Runge-Kutta (RK) scheme with a simple modification of the standard projection approach, which is…